Mathematics for FinancePYQ May 19 Series IIQuestion 1288 of 512
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The annual birth rate and death rate per 1000\displaystyle 1000 are 39.4\displaystyle 39.4 and 19.4\displaystyle 19.4 respectively. The number of years in which population will be doubled assuming that there is no immigration or emigration approximately.

Options

A30\displaystyle 30 years
B30\displaystyle 30 years
C35\displaystyle 35 years
D25\displaystyle 25 years
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Correct Answer

✅ Option c — 35\displaystyle 35 years

All Options:

  • A30\displaystyle 30 years
  • B30\displaystyle 30 years
  • C35\displaystyle 35 years
  • D25\displaystyle 25 years

Detailed Solution & Explanation

**Derivation of Population Doubling Time** Given: - Birth rate = 39.4\displaystyle 39.4 per 1,000\displaystyle 1,000 - Death rate = 19.4\displaystyle 19.4 per 1,000\displaystyle 1,000 **Step 1: Calculate the net annual growth rate (r\displaystyle r)** Net Growth Rate per 1,000=39.4−19.4=20\text{Net Growth Rate per 1,000} = 39.4 - 19.4 = 20 r=201000=2%=0.02 per annumr = \frac{20}{1000} = 2\% = 0.02 \text{ per annum} **Step 2: Set up the population doubling equation** (1+r)t=2(1 + r)^t = 2 (1.02)t=2(1.02)^t = 2 **Step 3: Solve for t\displaystyle t using logarithms** t=ln⁡(2)ln⁡(1.02)≈0.6931470.019803≈35 yearst = \frac{\ln(2)}{\ln(1.02)} \approx \frac{0.693147}{0.019803} \approx 35 \text{ years} Hence, **Option C** is the correct answer.

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